Question

By constructing truth tables, decide which of the following are tautologies.

(I) ~(P ^ ~P)

(II) P implies ~P

(III) (P ^ (p implies q)) implies q

B) show that (P implies Q) implies R is logically equivalent to
(~ P implies R) ^ (Q implies R)

Answer 1

Questions A

A tautology is a statement that is always true, no matter what. If you construct a truth table for a statement and all of the column values for the statement are true (T), then the statement is a tautology because it's always true!.

One first is correct.

Question B

Two statement forms are logically equivalent if, and only if, their resulting truth tables are identical for each variation of statement variables.

So both are logically equivalent.